Problem: Which of the following numbers is a factor of 180? ${7,10,11,13,14}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $180$ by each of our answer choices. $180 \div 7 = 25\text{ R }5$ $180 \div 10 = 18$ $180 \div 11 = 16\text{ R }4$ $180 \div 13 = 13\text{ R }11$ $180 \div 14 = 12\text{ R }12$ The only answer choice that divides into $180$ with no remainder is $10$ $ 18$ $10$ $180$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $10$ are contained within the prime factors of $180$ $180 = 2\times2\times3\times3\times5 10 = 2\times5$ Therefore the only factor of $180$ out of our choices is $10$. We can say that $180$ is divisible by $10$.